If it were me, here's what I'd do.

1. Refresh the Corian as chi flipper suggested.

2. Get a nonslip bath mat for inside the tub for showering.

3. Replace the flooring with something more updated. I personally would find a beautiful tile floor to go with what you have.

4. Replace the counter top with a piece of granite or other stone that works with your oak.

5. Get an undermount sink.

6. Get a new faucet. I would choose something in chrome and a wides spread faucet.

7. Replace the lighting overhead with something less dated.

8. Get new pulls for the cabinet and replace the towel holders and toilet paper holder.

9. Frame the mirror to match the wood.

The cabinets are fine as they are. Work with them.

To add to the above: brass in a satin or "champagne" finish is in style. Take a close look at what's available to match the quality of what you have now, as some new pieces are quite iightweight or just plastic with a shiny finish. Also, if the oak's clear finish has worn away, you can have it lightly sanded and then top-coated with a compatible clear finish.

Your oak looks a lot nicer than a lot of the honey oak out there. I agree with chiflipper and cpartist, above. Even your baseboards look like they are in good condition. If you do have problems with the finish wearing off, then refinish the cabinets and woodwork. One reason not to paint oak is that the grain often still shows through, requiring an extra coat of primer. Painting wooden cabinets in a home setting does not get you a hard paint finish. Instead, it often chips on edges over time. The best painted finishes require an industrial setting.

How do I find someone to refinish Corian? I know contacting a fabricator was mentioned, but we’re 100 miles from the nearest place with a population over 5,000. I’m having trouble finding anyone who seems knowledgeable.

Both contractors said that they wouldn’t refinish the oak because it’s too intricate and would take so much more time. They said it’s cheaper just to replace it. Does each and every inch have to be sanded down and stained? Is there a faster way to do this? (Gel stain etc)

Painting is the easiest way. Check Google for tips. I like oak painted cabinets with grain to show through the paint for a rustic look. People use chalk paint, it does not need sanding, but degloss.

Painting requires sanding first, possibly filling in of grooves, then at least one coat of primer, then two or more coats of paint. You have to be careful for about a month not to hit the finished surfaces with anything hard, as it will nick easily until "cured."

Refinishing requires that you sand everything down enough to de-gloss it if it is lightly scuffed. If you are leaving the color the same, you can then put on two coats of polyurethane finish.

If you need to stain the wood to change the color, you need to sand it down to bare wood. Some woods then require that you then put a conditioner on in order to get the stain to stick evenly. Then you stain the wood. After it dries, you need at least two coats of finish (polyurethane finish) over the stain. Research and try oil-based stains versus water-based stain. The water-based ones may require light sanding afterwards if they raised the grain.

I have used the newer water-based poly successfully on kitchen cabinets.